Distributed Weighted Least Squares Estimator Based on ADMM

TL;DR

This paper introduces a distributed weighted least squares estimator for sensor networks using ADMM, enabling consensus estimation without prior distribution knowledge, with proven convergence and effectiveness.

Contribution

It develops a novel distributed WLS estimation method based on ADMM, linking information filter and WLS, and ensures consensus in sensor networks.

Findings

Proven convergence of the proposed method.

Effective consensus estimation demonstrated.

Numerical simulations validate the approach.

Abstract

Wireless sensor network has recently received much attention due to its broad applicability and ease-of-installation. This paper is concerned with a distributed state estimation problem, where all sensor nodes are required to achieve a consensus estimation. The weighted least squares (WLS) estimator is an appealing way to handle this problem since it does not need any prior distribution information. To this end, we first exploit the equivalent relation between the information filter and WLS estimator. Then, we establish an optimization problem under the relation coupled with a consensus constraint. Finally, the consensus-based distributed WLS problem is tackled by the alternating direction method of multiplier (ADMM). Numerical simulation together with theoretical analysis testify the convergence and consensus estimations between nodes.